What is the conjecture

https://www.erdosproblems.com/601

For which limit ordinals $\alpha$ is it true that if $G$ is a graph with vertex set $\alpha$ then $G$ must have either an infinite path or independent set on a set of vertices with order type $\alpha$?

Status: open

Choose either option

• I plan on working on this conjecture
• This issue is up for grabs: I would like to see this conjecture added by somebody else